I see from your picture that you are using the LR Hanna phosphate checker, not the ULR checker. That checker has an error of +/- 0.04 ppm, plus 4% of the the reading. So, your PO4 could be 0.04 or lower, but not really zero. A lot of the methods that you are looking at to reduce NO3 rely on PO4 as well. These methods include carbon dosing and algae scrubbers. You have to look at your nutrients as limiting factors, i.e., things will only grow as much as the least amount of nutrient will let them. Since carbon dosing and algae scrubbers rely on organisms to consume nitrate, the nitrate reduction is limited by the available phosphate.
Looking at the pictures of your tank, you have a large bio load in fish. The fresh, self made food that you are feeding them is probably low in PO4, yet when consumed and excreted, is cycled to nitrate. I would suggest lighter feedings if possible, or supplementing that food with another food that is higher in phosphates. Flake foods usually have higher PO4.
The problem with reducing your NO3 with water changes is that you will also be reducing the already low PO4 by the same percentage. What you really need to do is figure out why you have such a nutrient imbalance and fix that.
Your tank looks good, so I would say that you have PO4 in there, just not enough for the LR checker to read consistently. Your NO3 may not be as high as you think as well. As @Ohashimz has said, you don't need to do anything drastic, just take it slow.
Looking at the pictures of your tank, you have a large bio load in fish. The fresh, self made food that you are feeding them is probably low in PO4, yet when consumed and excreted, is cycled to nitrate. I would suggest lighter feedings if possible, or supplementing that food with another food that is higher in phosphates. Flake foods usually have higher PO4.
The problem with reducing your NO3 with water changes is that you will also be reducing the already low PO4 by the same percentage. What you really need to do is figure out why you have such a nutrient imbalance and fix that.
Your tank looks good, so I would say that you have PO4 in there, just not enough for the LR checker to read consistently. Your NO3 may not be as high as you think as well. As @Ohashimz has said, you don't need to do anything drastic, just take it slow.